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1132                            Appendix VI.

Area  =   /    P. <fV


(logeV2 -

P. (5/2. The Reversed Heat Engine. — Let Fig. 1001
represent the two entropy-temperature diagrams of a perfect
engine (i) when taking in heat at rx and rejecting at r2 direct
working ; and (2) when taking in heat at rx and rejecting at r:
reversed working. The heat quantities are shewn by areas ; or by
temperatures only, since the entropy bases are equal. Let
B = _9_ A. Taking efficiency to mean ' energy utilised 4- energy
received,' we have :

Working j Effid         =   C,

Direct )               J        A


Working! Effid         _ A _   _^   = 10 .    ^
Reversed;              J        C       rx—ra       i

The result for direct working will not be questioned, for A is
the heat received from the boiler, and C is that utilised in the
cylinder. The case for reversed working needs a little thought.
Here the work done by the piston on the gas is the * energy
received' and is C, while the useful heat produced is two-fold :
the change of that work into heat, and the automatic supply from
the cold body represented by B. The total heat in the outgoing
gas is therefore C -f B = A.

Viewing the two engines quite separately, we see then, taking
the supposed figures, that when working direct we only utilise
one-tenth of the energy received; but on reversed working as a
heat supplier^ we return ten times the energy we expend. Nine of
I                          these ten parts have been extracted from the atmosphere, and we

have the curious result of an efficiency considerably greater than